I survey and assess the development of continuous-time methods in finance during the last 30 years. The subperiod 1969 to 1980 saw a dizzying pace of development with seminal ideas in derivatives securities pricing, term structure theory, asset pricing, and optimal consumption and portfolio choices. During the period 1981 to 1999 the theory has been extended and modified to better explain empirical regularities in various subfields of finance. This latter subperiod has seen significant progress in econometric theory, computational and estimation methods to test and implement continuous-time models. Capital market frictions and bargaining issues are being increasingly incorporated in continuous-time theory. THE ROOTS OF MODERN CONTINUOUS-TIME METHODS in finance can be traced back to the seminal contributions of Merton ~1969, 1971, 1973b! in the late 1960s and early 1970s. Merton ~1969! pioneered the use of continuous-time modeling in financial economics by formulating the intertemporal consumption and portfolio choice problem of an investor in a stochastic dynamic programming setting.

This paper presents a model of portfolio choice and stock trading volume with lossaverse investors. The demand function for risky assets is discontinuous and non-monotonic: as wealth rises beyond a threshold investors follow a generalized portfolio insurance strategy. This behavior is consistent with the evidence in favor of the disposition effect. In addition, loss-averse investors will not hold stocks unless the equity premium is quite high. The elasticity of the aggregate demand curve changes substantially, depending on the distribution of wealth across investors. In an equilibrium setting the model generates positive correlation between trading volume and stock return volatility, but suggests that this relationship should be non-linear.

impact of risk regulation on price

Risk management systems in current use treat the statistical relations governing asset returns as being exogenous, and attempt to estimate risk only by reference to historical data. These systems fail to take into account the feedback effect in which trading decisions impinge on prices. We investigate the consequences for asset price dynamics of the widespread adoption of such techniques. We illustrate through simulations of a general equilibrium model that, as compared to the case when such techniques are not used, prices are lower, have time paths with deeper and longer troughs, as well as a greater degree of estimated volatility. The magnitudes can sometimes be considerable. Far from promoting stability, widespread adoption of such techniques may have the perverse effect of exacerbating financial instability. First version. Subsequent updates of this paper will be posted on the authors ’ homepages or www.RiskResearch.org. All authors are at the Financial Markets Group, and

The effect of VaR-based risk management on asset prices and the volatility smile 1

Recognizing the drawbacks of Value-at-Risk (VaR), researchers have advocated the use of Conditional Value-at-Risk (CVaR). However, the current popularity of VaR and Stress Testing (ST) among bank regulators raises the question of whether a risk management system based on both VaR and ST constraints is an effective alternative to a system based on CVaR. We show that when the VaR and ST bounds are appropriately chosen and short selling is disallowed, the constraints lead to the selection of portfolios with relatively small CVaRs. However, when short selling is allowed, the constraints may not lead to the selection of such portfolios. Since large banks often have short positions in their trading books, regulators should be aware that the joint use of VaR and ST is unreliable in controlling CVaR for such banks.